Rapid increase in stroke incidence coupled with the high cost and limited availability of healthcare professionals has made stroke rehabilitation process inaccessible to many patients in developing countries. Stroke rehabilitation exercises are of critical importance in ensuring quick and lasting recovery. A machine learning-based system that can automatically identify the completion status of upper limb rehabilitation exercises is presented in this study. Proposed system can detect completion status of twelve hand and arm rehabilitation exercises: six hand, four forearm and two shoulder exercises. Accelerometers record the movement of the upper limb part being exercised in the form of data sequences. Six curve-fitting-based machine learning model types are trained and evaluated for their effectiveness in modelling these sequences. This resulted in a total of 216 models (i.e. 12 exercises × 3 axes of motion × 6 model types) being evaluated on three performance measures: SSE, RMSE and R². Best-performing model for each exercise is plugged into the proposed exercise completion status identification algorithm. System effectiveness is validated using four performance measures: accuracy, precision, recall and F1-score. Proposed system is demonstrated to be capable of detecting the exercise completion status with up to 90% accuracy. The proposed system is connected to cloud via an IoT interface with a dashboard type visualization system that allows for the healthcare professionals to remotely monitor the progress for each patient as well as carry out offline analysis. A game interaction interface is also provided to enable interaction with video games, helping in higher patient engagement while performing exercises.